Cold heart of oil burner? (6)
I believe the answer is:
chilli
'burner?' is the definition.
(I've seen this before)
'cold heart of oil' is the wordplay.
'cold' becomes 'chill' (chill is a kind of cold).
'heart of' says to take the centre.
The centre of 'oil' is 'i'.
'chill'+'i'='CHILLI'
(Other definitions for chilli that I've seen before include "Small hot-tasting pod" , "sort of powder" , "could make a hot meal" , "Give up completely" , "Hot food (that sounds cold!)" .)